Express the value 0.3 in the 32-bit floating point format that we discussed in class today. Feel free to only show fraction bits [22:15], rather than all the fraction bits. [22:0]. Notation: The symbol [22:15] signifies all 8 bits from bit 22 to bit 15.
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- 1. Write a C++ program that takes two binary numbers of 8 bits eachrepresented with the letters Z and O (for zero or one) and displays thesum in binary with Zs and Os. Do this by converting the numbers to ints,adding the its using +, displaying the 3 ints, then converting the sum toZ and Os and displaying the result. 1 a.) Redo number 1, by doing a bit-by-bit addition, not forgetting the carry. 1b.) Write a program to take two numbers represented with romannumerals and display the sum. Assume the sum will be less than 20.Hints: Ask the user to terminate each number with a semicolon and usechars to hold the roman ‘digits’.The numbers are I, II, III IV, V, VI, VII, VIII, IX, X, XI, XII, XIII, XIV, XV…isfive, Change the program to allow the sum to go up to 49 See how large a number you can handle. L is 50, C is 100, M is 1000. Using basic C++ int, char, if- else statements, and switch statements, please! no functions, or strings, or Cmath etc.Assume a 24-bit word on a computer. In these 24 bits, wewish to represent the value 295.1. a) How would the computer represent the decimal value295?2. b) If our computer uses 8-bit ASCII and even parity, howwould the computer represent the string 295?3. c) If our computer uses packed BCD with zero padding, howwould the computer represent the number +295?Please help me solve this problem with kind explanations :) We are running programs on a machine where values of type int have a 32-bit two's complement representation. Values of type float use the 32-bit IEEE format, and values of type double use the 64-bit IEEE format. We generate arbitrary integer values x, y, and z, and convert them to values of type double as follow: /* Create some arbitrary values */ int x = random(); int y = random(); int z = random(); /* Convert to double */ double dx = (double) x; double dy = (double) y; double dz = (double) z; For each of the following C expressions, you are to indicate whether or not the expression always yields 1. If it always yields 1, describe the underlying mathematical principles. Otherwise, give an example of arguments that make it yield 0. Note that you cannot use an IA32 machine running GCC to test your answers, since it would use the 80-bit extended-precision representation for both float and double. A. (double)(float) x == dx B. dx…
- 6. Convert the following numbers from unsigned binary notation to decimal notation, and from 6-bit 2's complement notation to decimal notation: i) 110011, ii) 001101, iii) 101101 7. Show how each of the following floating point values would be stored using IEEE-754 single precision (be sure to indicate the sign bit, the exponent, and the significand fields): a. 12.5 b. −1.5 c. 0.75 d. 26.625 8. The following is a representation of a decimal floating value using IEEE-754 single precision. Find out the value in decimal. 0 10000011 10101000000...0Consider the following code which includes a parity check for the third digit: C=(000,011,101,110). You get the third digit by adding the first two and then using the remainder on division by 2. Can this code detect and count single errors? how can this be implemented?CPU contains a special bit called the overflow bit , denoted by V. When CPU adds two binary integers, if their sum is out of range when interpreted in 2's complement representation, then V is set to _____, otherwise V is set to _______. Question 4 options: A. 0 : 0 B. 1 : 0 C. 0 : 1 D. 1 : 1 2 X = 0 0000 0000 1000 0000 0000 0000 0000 000 is an IEEE 754 single precision floating point number, what is the decimal value of X? Question 5 options: 1.5 × 2–127 0.5 × 2–127 1.5 × 2–126 0.5 × 2–126 None of the above
- Consider a 6-bit two’s complement representation. Fill in the box with question mark "?" in the following table. You don't need to care about "n/a." Number Binary Representation TMin + TMin ? Please input the binary representation in this format xxxxxx. For example, if the answer is 010010, please input 010010.7. Add the following two 8-bit binary numbers, producing an 8-bit result. Indicate the status of the carry and overflow bits at the end of the addition by circling the appropriate choices. The space in between is only for readability. 1101 0110 + 1001 0111 -------------- Overflow? Yes or No Carry? Yes or NoConsider the following floating point representation where each number has 2exponent bits and 5 fraction bits. The exponent bias is 1. Round each number tohave 3 fraction bits. Apply round-to-even and round-toward-zero modes.a. 1 10 11100b. 0 00 00101c. 1 01 10101i. Can you see a pattern for rounding floating point numbers when thenumber of exponent bits are intact?
- Consider an 8-bit floating point format. In this representation 4 bits are reserved for the mantissa and 3 bits are reserved for the exponent and 1 bit is reserved for the sign of the number. The exponent of the number is stored with a bias = 3. Express the decimal number 4.75 in this 8 bit floating point format. Write down the next bigger representable number in decimal base. B If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.75 Express the decimal number 4.75 in this 8 bit floating point format. [10] b) Write down the next bigger representable number in decimal base. [7.5] c) If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.75I could use some help converting this problem into code for IA32 x86 Assembly floatIsEqual - Compute f == g for floating point arguments f and g. Both the arguments are passed as unsigned int's, but they are to be interpreted as the bit-level representations of single-precision floating point values. If either argument is NaN, return 0 +0 and -0 are considered equal.1) Find the equivalent decimal value of the following floating-point representation using IEEE 754 standard single-precision (32-bit floating-point number with bias = 127) 1 0111 1111 1110 0000 0000 0000 0000 000 (The quiz is expecting a decimal numeric entry. It will automatically suppress leading and trailing zeros. It will display your answer with commas every third digit.) 2) Find an IEEE 754 floating-point representation of -74.2 decimal number. Enter 32 bits without a space. (The quiz is expecting a fill in the blank text string in the entry box and grades on an exact match with the expected result. The answer should be formatted as a 32-bit IEEE 745 binary number representation)